Optimal Execution Strategies in Limit Order Books with General Shape Functions

29 Pages Posted: 20 Nov 2009

See all articles by Aurélien Alfonsi

Aurélien Alfonsi

Université Paris Est - CERMICS

Antje Fruth

Technical University Berlin

Alexander Schied

University of Waterloo

Date Written: November 20, 2009

Abstract

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy of a risk-neutral investor, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience type.

Keywords: Liquidity risk, optimal portfolio liquidation, block trade execution, limit order book, market impact model, nonlinear price impact, order book resilience, market order

JEL Classification: G12, G32

Suggested Citation

Alfonsi, Aurélien and Fruth, Antje and Schied, Alexander, Optimal Execution Strategies in Limit Order Books with General Shape Functions (November 20, 2009). Available at SSRN: https://ssrn.com/abstract=1510104 or http://dx.doi.org/10.2139/ssrn.1510104

Aurélien Alfonsi

Université Paris Est - CERMICS ( email )

6 et 8 avenue Blaise Pascal
Marne-la-Vallée, Champs sur marne 77420
France

Antje Fruth

Technical University Berlin ( email )

Straße des 17
Berlin, 10623
Germany

HOME PAGE: http://www.math.tu-berlin.de/~fruth

Alexander Schied (Contact Author)

University of Waterloo ( email )

200 University Ave W
Waterloo, Ontario
Canada

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